A transformation for an -balanced

Author:
H. M. Srivastava

Journal:
Proc. Amer. Math. Soc. **101** (1987), 108-112

MSC:
Primary 33A30; Secondary 05A30

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897079-3

MathSciNet review:
897079

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Abstract: An interesting generalization of the familiar -extension of the Pfaff-Saalschütz theorem is proved and is applied, for example, to derive a reduction formula for a certain double -series. The main theorem (asserting the symmetry in and of a function defined in terms of an -balanced basic (or -) hypergeometric series by equation (8)) is essentially a -extension of Sheppard's transformation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897079-3

Keywords:
Pfaff-Saalschütz theorem,
basic (or -) hypergeometric series,
-balanced series,
Sheppard's transformation,
Gaussian (or -binomial) coefficient,
Jackson's sum,
-series identity,
Sears's transformation,
combinatorial analysis

Article copyright:
© Copyright 1987
American Mathematical Society